Josimar da Silva Rocha. The n-ary Adding Machine and Soluble Groups


Natural Sciences / Mathematics / Algebra

Submitted on: Mar 27, 2012, 17:44:18

Description: We describe under a variety of conditions abelian subgroups of the automorphism group A of the regular n-ary tree T which are normalized by the n-ary adding machine t=(e...,e,t)s where s is the n-cycle (0,1...,n-1). As an application, for n a prime number, and for n = 4 we prove that every finitely generated soluble subgroup of A containing t is an extension of a torsion-free metabelian group by a finite group.

The abstract of this article has been published in the "Intellectual Archive Bulletin" , March 2012, ISSN 1929-1329.

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The n-ary Adding Machine and Soluble Groups.pdf



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